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# Thermally Induced Stress in a Glass-Silicon Bonded MEMS Micro-Structure A Finite Element Analysis ( FEA ) using flexPDE

Thermally Induced Stress in a Glass-Silicon Bonded MEMS Micro-Structure A Finite Element Analysis ( FEA ) using flexPDE. Craig E. Nelson - Consultant Engineer. The purpose of this numerical experiment is to learn about the field distribution of stress and strain in a MEMS microstructure.

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## Thermally Induced Stress in a Glass-Silicon Bonded MEMS Micro-Structure A Finite Element Analysis ( FEA ) using flexPDE

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1. Thermally Induced Stress in a Glass-Silicon Bonded MEMS Micro-Structure A Finite Element Analysis ( FEA ) using flexPDE Craig E. Nelson - Consultant Engineer

2. The purpose of this numerical experiment is to learn about the field distribution of stress and strain in a MEMS microstructure. This knowledge helps the engineer to better understand the stress on a bond line as will occur when anodic bonding of glass and silicon is attempted. In this model, a high bonding temperature is impressed on all parts which subsequently cool to room temperature. As the material cools, it shrinks differing amounts in different materials and in different places within a given material, thus “freezing in” stress that, unless relieved, will exist for the life of the bonded part. Depending on circumstances, the bond line may be sufficiently stressed to fail during the cooling process.

3. Silicon Wafer Anodic Bond Line Glass Silicon Wafer Anodic Bond Line Model Geometry

4. Shrinkage Shrinkage Strained Structure – Shrinkage is Greatly Magnified

6. Strain Distribution Field – Horizontal Direction

7. Strain Distribution Field – Vertical Direction

8. Strain Distribution Field – Vector Plot

9. Stress Distribution Field – Horizontal Direction

10. Stress Distribution Field – Vertical Direction

11. Shear Stress Distribution Field

12. Stress Distribution Field – Tension

13. Principal Stress Distribution Field – Horizontal Component

14. Principal Stress Distribution Field – Vertical Component

15. Angle of Principal Stress Distribution Field

16. Von Mises Stress Distribution Field

17. Strain Distribution Field – Horizontal Component

18. Stress Distribution Field – Horizontal Component

19. Stress Distribution Field – Vertical Component

20. Summary and Conclusions A finite element model has been developed that allows insight into the field distribution of stress and strain in an anodic bonded glass-silicon MEMS microstructure. This knowledge helps the engineer to better understand the stress and strain on the glass-silicon bond line and other parts of the solution domain. The model could be further developed in many further ways.

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